# WRITING AN EQUATION AND CHECKING SOLUTIONS

To solve real world problems, always it is important to know how to write an equation which represents the given situation.

To write an equation for the given situation, first we have to understand the relationship between the quantities.

Using the relationship between the quantities, we have to write the equation which represents the given situation.

We can substitute a given value for the variable in a real-world equation to check if that value makes sense for the situation.

Example 1 :

Sarah used a gift card to buy \$47 worth of food. She has \$18 left on her gift card. Write an equation to represent this situation and use it to determine whether Sarah had \$65 or \$59 on the gift card before buying food.

Solution :

Step 1 :

Write a word equation based on the situation. Step 2 :

Rewrite the equation using a variable for the unknown quantity and the given values for the known quantities.

Let x be the amount on the card.

The amount spent and the amount left on the card are the known quantities. Substitute those values in the equation. Step 3 :

Substitute 65 and 59 for x to see which equation is true. So, the amount on Sarah’s gift card before she bought food was \$65.

Example 2 :

On Saturday morning, Owen earned \$24. By the end of the afternoon he had earned a total of \$62. Write an equation to represent the situation. Tell what the variable represents. Determine whether Owen earned \$38 or \$31 on Saturday afternoon.

Solution :

Step 1 :

Write a word equation based on the situation.

Amount earned on Saturday morning

Amount earned on Saturday afternoon

||

Total money earned

Step 2 :

Let x be the amount  earned by Owen between morning and afternoon

The amount earned in the morning and total amount earned by the end of the afternoon are known quantities. Substitute those values in the equation.

Then the word equation will become

24 + x  =  62

Step 3 :

Substitute 38 and 31 for x to see which equation is true. So, Owen earned \$38 on Saturday afternoon.

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